1. Field of Invention
The invention relates to magnetic imaging of live tissue. More specifically, it relates to the identifying and locating of double-layer using magnetic images.
2. Description of Related Art
Electric current source estimation is a common problem in various electromagnetic imaging technologies. One area of electromagnetic imaging is the imaging of electric fields emanating from living tissue. Living organisms generate electric impulses, which result in electric fields, and electric imaging (or electric field imaging) makes it possible to capture images of these electric fields (hereinafter termed electric images). Ideally, one would like to reconstruct an electric impulse from its captured electric field. Electric imaging has found wide application in the medical field.
As it is known in the art, an electric current generates a magnetic field. Thus, organisms that generate electric impulses also generate magnetic fields, and magnetic imaging (or magnetic field imaging) makes it possible to capture images of these magnetic fields (hereinafter termed magnetic images). The study of such magnetic fields in living organisms, or living tissue, is generally known as biomagnetism. Of particular interest in the field of biomagnetism is the magnetic imaging of the human brain and the human heart.
The development of electric imaging and magnetic imaging technology permits the detection and analysis of electrophysiological processes in the brain, heart and other nerve systems. Recording (i.e. imaging) of the electromagnetic fields from such tissues is typically accomplished by placing multiple electric (field) sensors or magnetic (field) sensors around the tissue being studied. For example, electroencephalography (EEG) uses electric sensors placed around the brain to record electric images of brain tissue, and electrocardiography (ECG or EKG) uses electric sensors placed over the chest to record electric images of heart tissue. Similarly, magnetoencephalography (MEG) uses magnetic sensors placed around the brain to record magnetic images of brain tissue, and magnetocardiography (MCG) uses magnetic sensors placed over the chest to record magnetic images of heart tissue. Examples of an MEG unit and an MCG unit are illustrated in FIGS. 1A and 1B, respectively.
With reference to FIG. 1A, an MEG system consists of a large number (usually 300 or less) of magnetic sensors arranged in a spherical shape (to be fitted around a human head) to provide a high spatial resolution for measurements. The MEG system measures magnetic fields created by brain nerve activity. Each magnetic sensor measures a one-dimensional (1D) magnetic waveform, Bz, in the radial direction.
With reference to FIG. 1B, an MCG system may include a small number (usually 64 or fewer) of magnetic sensors (each sensor is typically a Superconducting Quantum Interference Device, or SQUID) arranged as a sensor planar array. Each SQUID sensor measures a one-dimensional (1D) magnetic waveform (Bz) in the z direction, as illustrated by (x, y, z) axes. The MCG device is usually placed above and within 10 cm of a patient's chest in a location over the patient's heart. Electric current [i.e. electric impulse(s)] in the heart generates a magnetic field B that emanates out from the patient's torso. Each SQUID sensor measure the z-component (i.e. Bz) of the emanating magnetic field B that reaches it. That is, each SQUID sensor measures a 1D magnetic waveform in the z direction.
Compared to electric imaging (or recording) technology such as EEG and ECG, magnetic imaging technology such as MEG and MCG would be preferred due it being more non-invasive and providing a two-dimensional (2D) image (by virtual of the x-y plane of SQUID sensors) at a given point in time. Moreover, the magnetic field generated outside of the human body is not distorted in the direction perpendicular to the body surface (e.g. the radial direction in FIG. 1A and the z-direction in FIG. 1B), due to the magnetic property of body tissue. Thus magnetic imaging is more accurate and sensitive to weak electric activity within the body.
By way of example, the following discussion focuses on magnetic imaging of heart tissue, but it is to be understood that the following discussion is also applicable to magnetic imaging in general, and in particular, applicable to magnetic imaging of other living tissues.
Cardiac electric currents (or current impulses) are generated by electrophysiological processes in the heart. Localization of abnormal electric currents may be used in the diagnosing of ischemic diseases such as myocardial infarction, angina cordis, etc. It also benefits patients in the catheter lab for both treatment and follow-up, as is explained in “Forty Years of Magnetocardiology”, by F. Stroink, in Int. Conf. on Biomagnetism Advances in Biomagnetism, 28:1-8, 2010.
Traditionally, irregular cardiac electric activity, such as arrhythmia, is diagnosed by means of an electrocardiogram (ECG). However, an ECG only provides temporal information, and thus cannot localize abnormal electric impulse currents in the heart directly, even if the ischemic disease has been detected. One technique to attempt to localize electrical impulse currents is known as Body Surface Potential Mapping (BSPM), which uses a large number of electrodes (i.e., leads) to reconstruct a body surface potential map. This BSPM technique is explained in “Noninvasive Volumetric Imaging of Cardiac Electrophysiology”, by Wang et al., in CVPR, pages 2176-2183, 2009. The accuracy of BSPM electric current localization, however, is limited because the observed electrical signals can be distorted by the poor conductivity of body tissue.
The advent of the magnetocardiogram, or magnetocardiography, (MCG) made available more accurate measurements of cardiac electric currents, both spatially and temporally. An MCG is described above in reference to FIG. 1B.
In an MCG system, electromagnetic sensors (i.e. SQUID sensor) are arranged as a sensor planar array. Each electromagnetic sensor is a capture point, and hereinafter may be referred to as a “capture”. Each capture measures a 1D magnetic waveform in a direction perpendicular to the sensor planar array (i.e. the z-direction) emanating from the patient's chest (i.e. human torso). By aligning (or synchronizing) the depth measures (i.e. the 1D magnetic waveform) of the planar array of captures at a given depth in the z-direction (which may define an observation plane through the heart tissue), a 2D MCG map at the given depth may be constructed. The MCG system is usually placed five to ten centimeters above the patient's chest, and measures the patient's heart magnetic field in a non-invasive manner. Thus, the array of captures measure a collection of low resolution (hereinafter, low-res), two-dimensional MCG maps (or images) of electromagnetic activity.
MCG has a few advantages over ECG. First, the magnetic field generated by the heart's electric current impulses (hereinafter, currents, electric currents or electrical currents) is not distorted in the direction perpendicular to the body surface (i.e., the z direction), due to the magnetic property of body tissue. Thus MCG is more accurate and sensitive to weak electric activity in the early stage of heart disorders. Second, the MCG sensor array can localize the position of electric currents in the heart. Finally, MCG measurements are non-invasive. After forty years of research in MCG, cardiac electric current localization and high resolution visualization for MCG measurements are attracting more and more interest from both research and clinical areas.
However, there are a number of difficulties associated with MCG. A first difficulty is the great amount of electromagnetic noise that can obscure the small magnetic fields created in a human heart. This has been addressed, to some extent, by using a magnetically-shielded room to reduce background noise and by the introduction of a sensitive electromagnetic sensor, such as the superconducting quantum interference device (SQUID). Although these steps have helped, the raw readings nonetheless remain more noisy than desired.
Another difficulty is the limited number of electromagnetic sensors (i.e. SQUIDs) that may be used in an MCG system, which limits the resolution of an MCG map. As a result, the MCG system can typically produce only low resolution (low-res) 2D MCG maps. Typically, these low-res 2D MCG maps are not sufficient for diagnosis purposes. For example, a 64 channel Hitachi™ MCG system with a 25 mm sensor interval (as described in “Newly Developed Magnetocardiographic System for Diagnosing Heart Disease”, by Tsukada et al., in Hitachi Review, 50(1):13-17, 2001) only measures an 8×8 MCG map (i.e. it has an 8×8 array of 64 measurement points, or captures). One solution is to increase the number of sensors, but this is very difficult in practice due to the physical size of the sensors and system design.
One approach to overcoming this physical limitation is to approximate a high-resolution (hereinafter, high-res) magnetic image from the low-res image created by the limited number of magnetic sensors. Thus, a necessary step in MCG is generating a high-res, 2D MCG image, or map, from a low-res, 2D MCG image, or map.
Two image examples, L and R, of high-res 2D MCG images generated from low-res images are shown in FIG. 2. Left image L shows the tangential image of a generated high-res MCG image of a healthy heart. The maximal point (i.e. strongest point) within image L indicates the location (or source) of electric current in the heart. Thus, high-res MCG images permits doctors to directly “see” the electrical activity in the heart. Right image R shows the tangential image of a high-res MCG image of an unhealthy heart. It differs significantly from left image L of a healthy heart, and thus provides important cues for diagnosis. Compared to low-res MCG maps, high-res MCG images provide more diagnostic significance.
One way to generate a high-res magnetic field image from a low-res magnetic image is by interpolation. Most modern MCG systems use curve fitting interpolation methods between observed measurements of the electromagnetic sensors to construct high-res 2D MCG images from the low-res 2D MCG maps, such as described in “Magnetocardiographic Localization of Arrhythmia Substrates: A Methodology Study With Accessory Path-Way Ablation as Reference”, by B. A. S. et al., in Ann Noninvasive Electrocardiol, 10(2):152-160, 2005, and described in “Evaluation of an Infarction Vector by Magnetocardiogram: Detection of Electromotive Forces that Cannot be Deduced from an Electrocardiogram”, by Nomura et al, in Int. Congress Series, 1300:512-515, 2007. Unfortunately, the accuracy of curve fitting methods is typically limited.
Recently machine learning techniques have been used for high-res magnetic field image generation. An example is presented in Interpolation in MCG Mapping, IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, pages 4381-4384, 2005, S. Jiang et al. This approach illustrates learning nonlinear interpolation functions using neural networks.
As described above, magnetic imaging provides images of the electric field at a given time and depth within a tissue. Oftentimes, it would be beneficial to identify the electric current impulse (or current impulse) responsible for the observed magnetic field. In the high-res images described above (see FIG. 2, for example) one may identify the maximal point (i.e. strongest point) within a magnetic image as being indicative of the location (or source) of a current impulse.
Trying to identify the current impulse that generated an observed magnetic image is termed the inverse problem. That is, using the obtained magnetic field measurements at different sites, one attempts to estimate the location and moment of the current source that generated the observed (i.e. the measured) magnetic field. This is called the inverse problem. For example, Conversion of Magnetocardiographic Recordings Between Two Different Multichannel Squid Devices, IEEE Trans. on Biomedical Engineering, 47(7):869-875, 2000, by M. B. et al. describes tackling the inverse problem to reconstruct the 3D position, magnitude and orientation of current sources. Once the current source is known, the high-res magnetic field can be computed from the reconstructed current source by use of the Biot-Savart law. However, due to its poor initiation, this approach is often unreliable.
There are a number of other difficulties involved in addressing the inverse problem. According to the Helmholtz reciprocity principal, the inverse problem for MCG is an ill-posed problem unless the prior electric currents and their number are known. Nonetheless, several approaches towards addressing the inverse problem have been proposed.
For example, a trivia case that assumes a single electric current located at the world origin and far from the sensor array is described in Magnetocardiographic Localization of Arrhythmia Substrates: a Methodology Study with Accessory Pathway Ablation as Reference, Europace, 11(2):169-177, 2009, R. J. et al. This situation cannot be satisfied in practice.
In the case of estimating a large number of current sources, such as estimating nerve activity in the brain, the inverse problem can be put under constraints, such as describe in Magnetic Source Images Determined by a Lead-Field Analysis The Unique Minimum-Norm Least-Squares Estimation, IEEE Trans. Biomed Eng., 39(7):665-675, 1992, by J. Z. Wang et al. This approach requires solving a large scale non-linear optimization problem, which is often computationally expensive and may lead to undesired local optima without good initialization.
Alternatively, by considering the temporal information and signal-to-noise ratio, the inverse problem can by addressed by the beam-former and synthetic aperture magnetometery (SAM) methods, as described in MEG Inverse Problem with Leadfields, 15th Japan Biomagnetism Conference, 13(1):42-45, 2000, by A. Matani. These types of methods require a statistical analysis of specific current sources, and thus do not permit the use of a one-time, 2D magnetic field image without any assumptions on current sources.
Thus, addressing the inverse problem usually requires that it be simplified by making use of regularization methods (as described by Matani, above) and that the position of current sources be given a priory (as described in An Optimal Constrained Linear Inverse Method for Magnetic Source Imaging, Nuclear Science Symposium and Medical Imaging Conference, pages 1241-1245, 1993, by P. Hughett).
However, linear solutions to the inverse problem can be approximated in special cases where the current positions are fixed at uniform 3D grids, as put forth by J. Z. Wang et al. (cited above) and in Simulation Studies of Biomagnetic Computed Tomography, IEEE Trans. Biomed Eng., 40(4):317-322, 1993, C. Ramon et al.
C. Ramon et al. also show that the inverse problem can have over-constraints in the case of a single current source, which is popularly used in many applications of heart diseases diagnosis. But even in this case, the inverse problem is still a medium-scale nonlinear optimization process, which highly depends on the initialization and the number of independent constraints. However, the sparse magnetic measurement can only provide limited information for estimating good initialization and solving the inverse problem. For example, the 64-channel Hitachi MCG system described above only measures magnetic fields on an 8×8 grid with a 25 mm sensor interval.
As it would be understood, a captured magnetic image is likely comprised of a combination of multiple electric impulses at different depths, and not the result of a single electric current impulse. What is needed is a magnetic imaging system capable of providing information relating the composite of a plurality of electric impulses responsible for an observed magnetic field.
Also needed is a magnetic imaging system that provides a view of such combinations of electric impulses without placing impractical demands on computing resources or requiring a priori assumptions regarding the number and location of previous electric currents.